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* add agenteval-notebook for math problems and the blog post about it * update gitignore * updates to notebook * adding folder for the logs * adding math problems logs * adding folder for alfworld logs * added limitiation and future work to blog post * minor edits blog post * adding changes * reorg * modify the main notebook * modification of the main notebook * remove wrong notebook * uploading new notebook * update agenteval notebook * change the sample * Update agenteval_cq_math.ipynb * adding final changes to notebook * updated framework picture * Update index.mdx * Update index.md * Add files via upload * updates to notebool * revise the blog * revise the blog * update the agent img * revise the blog * revise the blog * Excluded model logs from the main branch, you can find them in agenteval branch * Fixed pre-commit formatting. * Update website/blog/2023-11-11-AgentEval/index.mdx Co-authored-by: Chi Wang <wang.chi@microsoft.com> * update gitignore * update index.mdx * update authors.yml by adding Negar and Julia * remove md file * remove md file * update gitignore * update authors file * pre-commit checks * pre-commit checks on authors.yml * pre-commit checks on authors.yml * update index.mdx * update authors.yml by adding Negar and Julia * updated the blog-post version 1 * updated the blog-post: TL;DR is ready * updated the blog-post: first part of introduction is ready * updated figures: typos on fig 1, changed terminology on the fig 2 * upadated the Framework part * fixed redering issues * upload zip file instead of single samples * update prealgebra.zip * update * upload * update z * update naming * update zip * update the agenteval notebook * update the notebook - removing unmercenary logs * updated fig 1 and references to it * updated fig 1 * incorporated PR comments * merged agenteval branch * final changes to the blog * updated taxonomy * update notebook * minor changes to the blog * Fixed formatting * Update the link in agenteval_cq_math.ipynb * update the blog and link in notebook * Update index.mdx * change folder name * Changes to be committed: modified: OAI_CONFIG_LIST_sample.txt * add sample OAI file * fix the url link to colab and typos * fix the url link to colab and typos * add authors * update profile pic * "update authors" * fixing the problem in test_groupchat.py * update the title lower case * reverting changes in setup.py * rerun pre-commit --------- Co-authored-by: Negar Arabzadeh <ngr.arabzadeh@gmail.com> Co-authored-by: Julia Kiseleva <jukisele@microsoft.com> Co-authored-by: afourney <adamfo@microsoft.com> Co-authored-by: Chi Wang <wang.chi@microsoft.com> Co-authored-by: Qingyun Wu <qingyun.wu@psu.edu>
33 lines
2.9 KiB
Plaintext
33 lines
2.9 KiB
Plaintext
{
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"problem": "Find all $x$ that satisfy the inequality $(2x+10)(x+3)<(3x+9)(x+8)$. Express your answer in interval notation.",
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"level": "Level 5",
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"type": "Algebra",
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"solution": "We have \\begin{align*} (2x+10)(x+3)&<(3x+9)(x+8) \\quad \\Rightarrow\n\\\\ 2(x+5)(x+3)&<3(x+3)(x+8) \\quad \\Rightarrow\n\\\\ 2(x+5)(x+3)-3(x+3)(x+8)&<0 \\quad \\Rightarrow\n\\\\ (2x+10-(3x+24))(x+3)&<0 \\quad \\Rightarrow\n\\\\ (-x-14)(x+3)&<0 \\quad \\Rightarrow\n\\\\ (x+14)(x+3)&>0.\n\\end{align*} This inequality is satisfied if and only if $(x+14)$ and $(x+3)$ are either both positive or both negative. Both factors are positive for $x>-3$ and both factors are negative for $x<-14$. When $-14<x<-3$, one factor is positive and the other negative, so their product is negative. Therefore, the range of $x$ that satisfies the inequality is $ \\boxed{(-\\infty, -14)\\cup(-3,\\infty)} $.",
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"correct_ans": "(-\\infty, -14)\\cup(-3,\\infty)",
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"problem_id": "0",
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"response_with_ans": "I apologize for the confusion in my previous message. Let's find the factorized form of the quadratic using Python code.\n\n```python\nfrom sympy import symbols, factor\r\nx = symbols('x')\r\nfactorized = factor(x**2 + 17*x + 42)\r\nfactorized\r\n```\n\nPlease run the Python code above to find the factorized form of the quadratic, and we can proceed to determine the intervals where the inequality holds true.",
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"round": 1,
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"messages": [
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{
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"content": "Find all $x$ that satisfy the inequality $(2x+10)(x+3)<(3x+9)(x+8)$. Express your answer in interval notation.",
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"role": "user"
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},
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"content": "First, let's simplify and isolate the inequality to solve for $x$. For this, we need to expand the expressions on both sides and then move everything to one side.\n\nStep 1: Expand the expressions on both sides\n$(2x+10)(x+3) = 2x^2 + 6x + 10x + 30 = 2x^2 + 16x + 30$\n$(3x+9)(x+8) = 3x^2 + 24x + 9x + 72 = 3x^2 + 33x + 72$\n\nStep 2: Move everything to one side\n$0 < 3x^2 + 33x + 72 - (2x^2 + 16x + 30) = x^2 + 17x + 42$\n\nNow we need to find the factorized form of the quadratic inequality $x^2 + 17x + 42 > 0$ and then find intervals where the inequality holds true.\n\nLet's first find the factorized form of the quadratic:",
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"role": "assistant"
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},
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{
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"content": "",
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"role": "user"
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},
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{
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"content": "I apologize for the confusion in my previous message. Let's find the factorized form of the quadratic using Python code.\n\n```python\nfrom sympy import symbols, factor\r\nx = symbols('x')\r\nfactorized = factor(x**2 + 17*x + 42)\r\nfactorized\r\n```\n\nPlease run the Python code above to find the factorized form of the quadratic, and we can proceed to determine the intervals where the inequality holds true.",
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"role": "assistant"
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}
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],
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"time": 24.91333508491516,
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"check_result": "the reply doesn't contain an answer.",
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"is_correct": false,
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"trial": -1
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}
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